Journal of Philosophical Logic 43 (5):827-834 (2014)

Graham Leach-Krouse
Kansas State University
In a recent paper , Urbaniak and Cieśliński describe an analogue of the Yablo Paradox, in the domain of formal provability. Just as the infinite sequence of Yablo sentences inherit the paradoxical behavior of the liar sentence, an infinite sequence of sentences can be constructed that inherit the distinctive behavior of the Gödel sentence. This phenomenon—the transfer of the properties of self-referential sentences of formal mathematics to their “unwindings” into infinite sequences of sentences—suggests a number of interesting logical questions. The purpose of this paper is to give a precise statement of a conjecture from Cieśliński and Urbaniak regarding the unwinding of the Rosser sentence, and to demonstrate that this precise statement is false. We begin with some preliminary motivation, introduce the conjecture against the background of some related results, and finally, in the last section, move on to the proof, which adapts a method used by Solovay and Guaspari
Keywords Paradoxes  Incompleteness  Truth  Yablo’s paradox  Gödel’s theorem  Rosser’s theorem  Self-reference  Well-foundedness
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DOI 10.1007/s10992-013-9291-5
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References found in this work BETA

Arithmetization of Metamathematics in a General Setting.S. Feferman - 1966 - Journal of Symbolic Logic 31 (2):269-270.
Dangerous Reference Graphs and Semantic Paradoxes.Landon Rabern, Brian Rabern & Matthew Macauley - 2013 - Journal of Philosophical Logic 42 (5):727-765.
Gödelizing the Yablo Sequence.Cezary Cieśliński & Rafal Urbaniak - 2013 - Journal of Philosophical Logic 42 (5):679-695.
Rosser Sentences.D. Guaspari - 1979 - Annals of Mathematical Logic 16 (1):81.

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Citations of this work BETA

Rosser-Type Undecidable Sentences Based on Yablo’s Paradox.Taishi Kurahashi - 2014 - Journal of Philosophical Logic 43 (5):999-1017.
Diagonal Arguments and Fixed Points.Saeed Salehi - 2017 - Bulletin of the Iranian Mathematical Society 43 (5):1073-1088.
On Rosser's Provability Predicates.Taishi Kurahashi - 2014 - Journal of the Japan Association for Philosophy of Science 41 (2):93-101.

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